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Ahlfors-Beurling operator on radial functions

We give a simple proof of a sharp bound of Ahlfors--Beurling operator on complex-valued radial functions. In the language of the Calculus of Variation we prove a certain estimates for stretch and twist functions. Our estimate go slightly beyond this case. This article was written in February 2009 and then delivered at a seminar talk at UW, Madison on February, 2009.

preprint2012arXivOpen access
Alexander Volberg
math.OCmath.PRmath.CA
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Alexander Volberg

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